Thermoeconomic cost optimization of superconducting magnets for proton therapy gantries

A compact gantry delivering 70-220 MeV protons with fixed field in the superconducting magnets could reduce the cost and improve the adoption of proton therapy. While a number of magnet and cryogenics designs have been proposed, the combined capital and operating costs of state-of-the-art superconducting materials have not been analyzed. In response, we develop a thermoeconomic model of a multi-stage, conduction cooled gantry lattice and analyze the cryocooler operating cost, cryocooler capital cost and conductor capital cost for Nb-Ti, Nb3Sn, REBCO and Bi-2223 over a continuous range of magnet temperatures, and a differential evolution algorithm is used to identify the optimal combination of thermal intercept temperatures. Although Nb3Sn yields the lowest Net Present Value (NPV) of $111.7k at a magnet temperature of 9.4 K, the optimized Bi-2223 design at 12.8 K approaches the realm of commercial feasibility by offering improved thermal stability and forgoing the need for costly conductor heat treatment and magnet quench training. Furthermore, it was found that Nb3Sn was more cost effective than Nb-Ti and that REBCO was not economically viable for the parameters of this investigation. The thermoeconomic model developed herein can optimize conductor choices, magnet temperatures and thermal staging which has value for any conduction-cooled superconducting magnet